Graphing an Inequality on a Number Line: A Parenthesis or a Square Bracket?

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Collin Doyle
Mrs. Perino
Math 48A.01
11 January 2013

Homework 1.2: P. 19-21 #’s 23-24, 66-67, 70, 73, 74a-b, 76

23) Problem: Explain how to determine whether a parenthesis or a square bracket is used when graphing an inequality on a number line.

Solution: a. Parenthesis: indicate a range of values, open interval, I think of parenthesis as being the parent that is more open to given their child toys and bending the rules.
b. Brackets: has limits between two numbers, closed interval, I think of brackets as the stern parent who enforces the rules to the highest degree.

24)Problem: The three-part inequality a < x < b means “a is less than x, and x is less than b.” Which one of the following inequalities is not satisfied by some real number x?
A. -3 < x < 5B. 0 < x < 4
C. -3 < x < -2D. -7 < x < -10

Solution: D, because -10 is less than -7 and x is greater than -7 which also means that x is also greater than -10.

66)Problem: If f(3) = -9.7, identify a point on the graph of f.

Solution: (3,-9.7), f(3) is f(x) which means that 3 is the x-value and -9.7 is the y-value.

67)Problem: If the point (7,8) lies on the graph of f, then f(___) = ____.

Solution: f(7) = 8, this problem is the reverse of the problem before, you plug in the x-value (7) into x in f(x) and then plug in the y-value (8) in for the y.

70)Problem: Use the graph of y = f(x) to find each function value: a. f(-2), b. f(0), c. f(1), and d. f(4).

Solution: f(-2)= (-2,5)
f(0)= (0,0)
f(1)= (1,2)
f(4)= (4,4)

73)Problem: Explain each term in your own words.
a. Relation
b. Function
c. Domain of a function
d. Range of a function
e. Independent variable
f. Dependent variable

Solution: a. Relation: one set of ordered pairs
b. Function: relates an input to an output
c. Domain of a function: the...
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